Simplifying Algebraic Expressions11-1

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Simplifying Algebraic Expressions11-1

Warm UpSimplify.

2011

834. 17 + 8 20 2

3. 6 + 9 10 + 32. 16 8 + 4 11. 9 + 13 5 + 3

Simplifying Algebraic Expressions11-1

Problem of the DayRay and Katrina are wandering through the wildlife preserve. They observe and count a total of 15 wild turkeys and deer and a total of 46 legs. How many of each did they see? 7 turkeys, 8 deer

Simplifying Algebraic Expressions11-1

Learn to combine like terms in an expression.

Simplifying Algebraic Expressions11-1

Vocabularytermslike termsequivalent expressionssimplify

Simplifying Algebraic Expressions11-1

Terms in an expression are separated by plus or minus signs.

Like terms can be grouped together because they have the same variable raised to the same exponents.

Equivalent expressions have the same value for all values of the variables.Constants such as 4, 0.75, and 11 are like terms because none of them have a variable.

Helpful Hint

Simplifying Algebraic Expressions11-1

To simplify an expression, perform all possible operations, including combining like terms.

Simplifying Algebraic Expressions11-1

Combine like terms.

Additional Example 1: Combining Like Terms To Simplify

Identify like terms.Combine coefficients: 14 – 5 = 9

A. 14a – 5a 9a

B. 7y2 + 8 – 3y2 – 1 + y Identify like terms; the coefficient of y is 1, because 1y = y.

Combine coefficients: 7 – 3 = 4 and 8 – 1 = 7

4y2 + y + 7

Simplifying Algebraic Expressions11-1

Combine like terms.

Additional Example 2A: Combining Like Terms in Two-Variables Expressions

Identify like terms.

Combine coefficients.

5t2 + 7p – 3p – 2t2

3t2 + 4p

5t2 + 7p – 3p – 2t2

Simplifying Algebraic Expressions11-1

Combine like terms.

Additional Example 2B: Combining Like Terms in Two-Variable Expressions

No like terms.

4m3 + 9n – 2

4m3 + 9n – 2

Simplifying Algebraic Expressions11-1

The Distributive Property states that a(b + c) = ab + ac for all real numbers a, b, and c. For example, 2(3 + 5) = 2(3) + 2(5).

Remember!

Simplifying Algebraic Expressions11-1

Simplify 6(5 + n) – 2n.

Additional Example 3: Using the Distributive Property to Simplify

Distributive Property.

Multiply.

6(5 + n) – 2n

30 + 6n – 2n6(5) + 6(n) – 2n

30 + 4n Combine coefficients: 6 – 2 = 4.

Simplifying Algebraic Expressions11-1

Solve x + 3x = 48.

Additional Example 4: Combining Like Terms to Solve Algebraic Equations

Identify like terms. The coefficient of x is 1.

Combine coefficients: 1 + 3 = 4

x + 3x = 48

4x = 484x = 48

x = 12

Divide both sides by 4.4 4

Simplifying Algebraic Expressions11-1

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Simplifying Algebraic Expressions11-1Lesson Quiz

Combine like terms.

1. 3x2 + 4 + 2x2 2. 13k + 6 – 8m + 9 + k

Simplify.

3. 4(3x + 6) – 7x 4. 6(x + 5) + 3x Solve.5. 6y + y = 42 6. The Accounting Department ordered 15 boxes of pens. The Marketing Department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens?

14k – 8m + 15

y = 6

5x2 + 4

5x + 24 9x + 30

$3

Simplifying Algebraic Expressions11-1

1. Combine like terms. 4p + 13 + 11pA. 15p2 + 13B. 15p + 13C. 28p

D. 28

Lesson Quiz for Student Response Systems

Simplifying Algebraic Expressions11-1

2. Combine like terms. 15t + 9 – 7s + 10 + 5t A. 15t – 7s – 1B. 15t – 7s + 1C. 20t – 7s + 19D. 20t + 7s + 19

Lesson Quiz for Student Response Systems

Simplifying Algebraic Expressions11-1

3. Simplify 7(4m + 9) – 9m.A. 19m + 9B. 19m + 63C. 37m + 9D. 37m + 63

Lesson Quiz for Student Response Systems

Simplifying Algebraic Expressions11-1

4. Solve 11v + 2v = 65.A. v = 2B. v = 5C. v = 7D. v = 11

Lesson Quiz for Student Response Systems